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Importance of fluid inertia for the orientation of spheroids settling in turbulent flow

Published online by Cambridge University Press:  10 January 2020

Muhammad Zubair Sheikh Open the ORCID record for Muhammad Zubair Sheikh [Opens in a new window] ,
Kristian Gustavsson Open the ORCID record for Kristian Gustavsson [Opens in a new window] ,
Diego Lopez Open the ORCID record for Diego Lopez [Opens in a new window] ,
Emmanuel Lévêque Open the ORCID record for Emmanuel Lévêque [Opens in a new window] ,
Bernhard Mehlig Open the ORCID record for Bernhard Mehlig [Opens in a new window] ,
Alain Pumir Open the ORCID record for Alain Pumir [Opens in a new window]  and
Aurore Naso Open the ORCID record for Aurore Naso [Opens in a new window]
Muhammad Zubair Sheikh
Affiliation:
Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, 69342Lyon, France Department of Mechanical Engineering, University of Engineering and Technology, Lahore-54890, Pakistan
Kristian Gustavsson
Affiliation:
Department of Physics, Gothenburg University, 41296Gothenburg, Sweden
Diego Lopez
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, Université Claude Bernard, CNRS, INSA de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, 69134Écully, France
Emmanuel Lévêque
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, Université Claude Bernard, CNRS, INSA de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, 69134Écully, France
Bernhard Mehlig
Affiliation:
Department of Physics, Gothenburg University, 41296Gothenburg, Sweden
Alain Pumir
Affiliation:
Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, 69342Lyon, France
Aurore Naso*
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, Université Claude Bernard, CNRS, INSA de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, 69134Écully, France
*
†Email address for correspondence: [email protected]
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Abstract

How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid that is set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent fluid-velocity gradients, on the other hand, tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that the particle tends to settle with its narrow edge first, therefore minimising the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating fluid-velocity gradients. We ask under which circumstances either one or the other dominates. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds-number flows. In this case non-spherical particles tend to settle with orientations maximising drag. But when the Reynolds number is small, then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its narrow edge first, minimising the drag.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A9
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Almondo, G., Einarsson, J., Angilella, J. R. & Mehlig, B. 2018 Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear. Phys. Rev. Fluids 3, 064307.CrossRefGoogle Scholar
Anand, P., Ray, S. S. & Subramanian, G.2019 Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence, Preprint, arXiv:1907.02857.Google Scholar
Bagheri, G. & Bonadonna, C. 2016 On the drag of freely falling non-spherical particles. Powder Technol. 301, 526–544.CrossRefGoogle Scholar
Bec, J., Homann, H. & Ray, S. S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112, 184501.CrossRefGoogle ScholarPubMed
Borgnino, M., Gustavsson, K., Lillo, F. D., Boffetta, G., Cencini, M. & Mehlig, B. 2019 Alignment of spheroidal self-propelled particles swimming in turbulent flows. Phys. Rev. Lett. 123, 138003.Google Scholar
Brenner, H. 1961 The Oseen resistance of a particle of arbitrary shape. J. Fluid Mech. 11, 604–610.CrossRefGoogle Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27 (3), 035101.CrossRefGoogle Scholar
Candelier, F., Einarsson, J. & Mehlig, B. 2016 Rotation of a small particle in turbulence. Phys. Rev. Lett. 117, 204501.CrossRefGoogle Scholar
Candelier, F., Mehlig, B. & Magnaudet, J. 2019 Time-dependent lift and drag on a rigid body in a viscous steady linear flow. J. Fluid Mech. 864, 554–595.CrossRefGoogle Scholar
Chen, J. P. & Lamb, D. 1994 The theoretical basis for the parametrization of ice crystal habits: growth by vapor deposition. J. Atmos. Sci. 51, 1206–1221.2.0.CO;2>CrossRefGoogle Scholar
Chevillard, L. & Meneveau, L. 2013 Orientation dynamics of small, tiaxial-ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571–596.CrossRefGoogle Scholar
Cox, R. G. 1965 The steady motion of a particle of arbitrary shape at small Reynolds numbers. J. Fluid Mech. 23, 625–643.CrossRefGoogle Scholar
Dabade, V., Marath, N. K. & Subramanian, G. 2015 Effects of inertia and viscoelasticity on sedimenting anisotropic particles. J. Fluid Mech. 778, 133–188.CrossRefGoogle Scholar
Ducasse, L. & Pumir, A. 2010 Inertial particle collisions in turbulent synthetic flows: quantifying the sling effect. Phys. Rev. E 80, 066312.Google Scholar
Durham, W. M., Climent, E., Barry, M., Lillo, F. D., Boffetta, G., Cencini, M. & Stocker, R. 2013 Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4, 2148.CrossRefGoogle ScholarPubMed
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1992 Kinematic simulation of homogeneous turbulence by unsteady random fourier modes. J. Fluid Mech. 236, 281–318.CrossRefGoogle Scholar
Good, G. H., Ireland, P. J., Bewley, G., Bodenschatz, E., Collins, L. R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.CrossRefGoogle Scholar
Gustavsson, K., Berglund, F., Johnsson, P. R. & Mehlig, B. 2016 Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence. Phys. Rev. Lett. 116, 108104.CrossRefGoogle ScholarPubMed
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014a Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows. Phys. Rev. Lett. 112, 014501.CrossRefGoogle Scholar
Gustavsson, K., Jucha, J., Naso, A., Lévêque, E., Pumir, A. & Mehlig, B. 2017 Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence. Phys. Rev. Lett. 119, 254501.CrossRefGoogle ScholarPubMed
Gustavsson, K., Sheikh, M. Z., Lopez, D., Naso, A., Pumir, A. & Mehlig, B. 2019 Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence. New J. Phys. 21, 083008.CrossRefGoogle Scholar
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014b Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112, 214501.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Kluwer.Google Scholar
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flows. J. Fluid Mech. 651, 81–91.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.CrossRefGoogle Scholar
Jucha, J., Naso, A., Lévêque, E. & Pumir, A. 2018 Settling and collision between small ice crystals in turbulent flows. Phys. Rev. Fluids 3, 014604.CrossRefGoogle Scholar
Khayat, R. E. & Cox, R. G. 1989 Inertia effects on the motion of long slender bodies. J. Fluid Mech. 209, 435–462.CrossRefGoogle Scholar
Kim, S. & Karrila, S. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Kiørboe, T. 2001 Formation and fate of marine snow: small-scale processes with large-scale implications. Sci. Mar. 65, 57–71.CrossRefGoogle Scholar
Klett, J. D. 1995 Orientation model for particles in turbulence. J. Atmos. Sci. 52, 2276–2285.2.0.CO;2>CrossRefGoogle Scholar
Kramel, S.2017 Non-spherical particle dynamics in turbulence. PhD thesis, Wesleyan University.Google Scholar
Landau, L. D. & Lifschitz, E. M. 1976 Mechanics. Buttlerworth-Heinemann.Google Scholar
Lopez, D. & Guazzelli, E. 2017 Inertial effects on fibers settling in a vortical flow. Phys. Rev. Fluids 2, 024306.CrossRefGoogle Scholar
Marchioli, C., Fantoni, M. & Soldati, A. 2010 Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22 (3), 033301.CrossRefGoogle Scholar
Maxey, M. R. 1983 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441.CrossRefGoogle Scholar
Naso, A., Jucha, J., Lévêque, E. & Pumir, A. 2018 Collision rate of ice crystals with water droplets in turbulent flows. J. Fluid Mech. 845, 615–641.CrossRefGoogle Scholar
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12, 033040.CrossRefGoogle Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Petrol. 63, 835–838.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. 2012 Rotation rate of rods in turbulent fluid flows. Phys. Rev. Lett. 109, 134501.CrossRefGoogle Scholar
Pruppacher, H. R. & Klett, J. D. 1997 Microphysics of Clouds and Precipitation, 2nd edn. Kluwer Academic.Google Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.CrossRefGoogle Scholar
Ruiz, J., Macias, D. & Peters, F. 2004 Turbulence increases the average settling velocity of phytoplankton cells. Proc. Natl Acad. Sci. USA 101, 17720–17724.CrossRefGoogle ScholarPubMed
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibers in isotropic turbulent flows. J. Fluid Mech. 540, 143–173.CrossRefGoogle Scholar
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014a Orientation statistics and settling velocity if ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56.CrossRefGoogle Scholar
Siewert, C., Kunnen, R. P. J. & Schröder, W. 2014b Collision rates of small ellipsoids settling in turbulence. J. Fluid Mech. 758, 686–701.CrossRefGoogle Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.CrossRefGoogle Scholar
Yang, P., Liou, K.-N., Bi, L., Liu, C., Yi, B. & Baum, B. A. 2015 On the radiative properties of ice clouds: light scattering, remote sensing, and radiation parametrization. Adv. Atmos. Sci. 32, 32–63.CrossRefGoogle Scholar
Zhan, C., Sardina, G., Lushi, E. & Brandt, L. 2014 Accumulation of motile elongated micro-organisms in turbulence. J. Fluid Mech. 739, 22–36.CrossRefGoogle Scholar